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c2 Bode Plot
Figure P616
R1 L C R2 + V ( jv) o
617 The circuit shown in Figure P617 is a
second-order lter because it has two reactive components (L and C) A complete solution will not be attempted However, determine: a The behavior of the voltage transfer function or gain at extremely high and low frequencies b The output voltage Vo if the input voltage has a
Vi ( jv)
Figure P618
Part I
Circuits
L + Vi ( jv) C R + V ( jv) o
RS C1
+ Vi ( jv) _
L1 C2 RL + V ( jv) o
(d) (d)
Figure P619
R1 L C R2 + V ( jv) o
620 In the circuit shown in Figure P620, determine:
a The voltage transfer function in the form Hv (j ) = Hvo Vo [j ] = Vi [j ] 1 jf ( ) C = 047 F
Vi ( jv)
b The gain or insertion loss in the pass-band in dB if
R1 = R2 = 16
Figure P618
619 Determine if each of the circuits shown in Figure
P619 is a low-pass, high-pass, band-pass, or band-stop (notch) lter
c The cutoff frequency d The Bode plot, ie, a semilog plot where the magnitude [in dB!] of the transfer function is plotted on a linear scale as a function of frequency on a log scale
Ii(v) + RS Vi ( jv) + _ L1 C L2 RL + V ( jv) o Vi ( jv) R1 C R2
Io(v) + V ( jv) o
Figure P620
621 The circuit shown in Figure P621 is a high-pass
lter in which R1 = 100 R2 = 50 RL = 100 C = 80 nF
RS L1 Vi ( jv) + _
C L2 RL + V ( jv) o
Determine: a The magnitude of the voltage transfer function, ie, the gain or insertion loss, at very low and at very high frequencies b The two cutoff frequencies
RS Vi ( jv) + _
C1 L
C2 RL + V ( jv) o + R1
R2 RL
+ V ( jv) o
Vi ( jv) (c)
Figure P619
Figure P621
6
Frequency Response and System Concepts
622 Determine, for the lter circuit shown in Figure
P622: a If this is a low-pass, high-pass, band-pass, or band-stop lter b The magnitude (in dB!) of the voltage transfer function gain (or gain or insertion loss) in the pass-band if: L = 11 mH R1 = 22 k C = 047 nF R2 = 38 k
625 In the lter circuit shown in Figure P625:
RS = 5 k RL = 5 k C = 56 nF L = 9 H
Determine: a An expression for the voltage transfer function: Hv (j ) = Vo (j ) Vi (j )
L R2 C
+ V ( jv) o
Vi ( jv)
b The resonant frequency c The cutoff frequencies d The magnitude of the voltage transfer function (gain) at the two cutoff frequencies and the resonant frequency e The bandwidth and Q f The magnitude of the voltage transfer function at high, resonant, and low frequencies without using the expression above
Figure P622
623 In the lter circuit shown in Figure P623:
RS = 100 Rc = 400 C = 05 nF RL = 5 k L = 1 mH
+ Vi ( jv)
Rs C L RL + V ( jv) o
Determine the magnitude, in dB, of the voltage transfer function or gain at: a Very high and very low frequencies b The resonant frequency c What type of lter is this
Figure P625
626 In the lter circuit shown in Figure P625:
RS = 5 k RL = 5 k C = 05 nF L = 1 mH
L Rc C L RL + V ( jv) o
Determine: a An expression for the voltage transfer function: Hv (j ) = Vo (j ) Vi (j )
Vi ( jv)
Figure P623
624 In the lter circuit shown in Figure P623:
RS = 100 Rc = 4 C = 05 nF RL = 5 k L = 1 mH
b The resonant frequency c The cutoff frequencies d The magnitude of the voltage transfer function (gain) at the two cutoff frequencies and the resonant frequency e The bandwidth and Q f The magnitude of the voltage transfer function at high, resonant, and low frequencies without using the expression above
Determine the magnitude, in dB, of the voltage transfer function or gain at: a High frequencies b Low frequencies c The resonant frequency d What type of lter is this
627 In the lter circuit shown in Figure P627:
RS = 500 Rc = 4 k C = 5 pF RL = 5 k L = 1 mH
Determine the magnitude, in dB, of the voltage transfer
Part I
Circuits
function or gain at: H (j ) = a b c d Vo (j ) Vi (j )
630 In the lter circuit shown in Figure P628, derive
the equation for the voltage transfer function in standard form Then, if Rs = 44 k C = 08 nF RL = 600 L = 2 H r = 25 Mrad/s
High frequencies Low frequencies The resonant frequency What type of lter is this
C + Vi ( jv) Rs
determine the cutoff frequencies, bandwidth, and Q
631 In the bandstop (notch) lter shown in Figure
P631: L = 04 mH Rc = 100 C = 1 pF Rs = RL = 38 k
L RL
+ V ( jv) o
Determine: a An expression for the voltage transfer function or gain in the form: Hv (j ) = Vo (j ) 1 + jf1 ( ) = Ho Vi (j ) 1 + jf2 ( )
Figure P627
628 In the lter circuit shown in Figure P628, derive
the equation for the voltage transfer function in standard form Then, if RS = 500 C = 5 pF RL = 5 k L = 1 mH
b The magnitude of the voltage transfer function or gain at high and low frequencies and at the resonant frequency c The resonant frequency d The four cutoff frequencies
determine the: a Magnitude, in dB, of the voltage transfer function or gain at: Vo (j ) H (j ) = Vi (j ) at high and low frequencies and at the resonant frequency b Resonant and cutoff frequencies
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